Flexible signal denoising via flexible empirical Bayes shrinkage

TL;DR

This paper introduces a flexible empirical Bayes shrinkage method for non-parametric signal denoising, capable of handling heteroskedasticity and various data types, with competitive results demonstrated through applications and an R package implementation.

Contribution

It develops a more flexible and stable empirical Bayes shrinkage approach for signal denoising, addressing limitations of previous methods in distribution assumptions and heteroskedastic data handling.

Findings

Competitive performance with existing methods

Effective smoothing of Poisson and heteroskedastic Gaussian data

Implementation available in R package smashr

Abstract

Signal denoising---also known as non-parametric regression---is often performed through shrinkage estimation in a transformed (e.g., wavelet) domain; shrinkage in the transformed domain corresponds to smoothing in the original domain. A key question in such applications is how much to shrink, or, equivalently, how much to smooth. Empirical Bayes shrinkage methods provide an attractive solution to this problem; they use the data to estimate a distribution of underlying "effects", hence automatically select an appropriate amount of shrinkage. However, most existing implementations of Empirical Bayes shrinkage are less flexible than they could be--both in their assumptions on the underlying distribution of effects, and in their ability to handle heterskedasticity---which limits their signal denoising applications. Here we address this by taking a particularly flexible, stable and computationally convenient Empirical Bayes shrinkage method, and we apply it to several signal denoising problems. These applications include smoothing of Poisson data and heteroskedastic Gaussian data. We show through empirical comparisons that the results are competitive with other methods, including both simple thresholding rules and purpose-built Empirical Bayes procedures. Our methods are implemented in the R package smashr, "SMoothing by Adaptive SHrinkage in R," available at https://www.github.com/stephenslab/smashr